Secret sharing generally involves the distribution of a secret among a group of recipients using cryptographic methods. Each recipient typically obtains one or more shares of the secret. A share is information which is derived from the secret. Anyone with fewer than K shares (K being the threshold) is unable to reconstruct the secret. However, someone with at least K shares is able to reconstruct the secret from those shares.
Perfect secret sharing (PSS) is a scheme in which an adversary in possession of fewer than K shares learns no information about the secret in an information-theoretic sense, i.e., even if the adversary has unbounded computational resources. For PSS, the size of the share depends on the size of the underlying secret. In particular, the size of every participant's share must be at least that of the secret itself. Various PSS schemes are described the following publications: E. F. Brickell and D. R. Stinson, “Some improved bounds on the information rate of perfect secret sharing schemes”, Journal of Cryptology, 5:153-166, 1992; R. M. Capocelli, A. D. Santis, L. Gargano, and U. Vaccaro, “On the size of shares for secret sharing schemes”, Journal of Cryptology, 6:157-167, 1993; E. D. Karnin, J. W. Greene, and M. E. Hellman, “On secret sharing systems”, IEEE Transactions on Information Theory, 29(1):35-41, 1983; and A. Shamir, “How to share a secret”, Communications of the ACM, 22(11):612-613, 1979, the contents and teachings of which are hereby incorporated by reference in their entirety.
In the context of radio frequency identification (RFID) tags, one could apply a PSS scheme so that an RFID tag periodically emits a share of RFID tag information (i.e., the secret) in an attempt to conceal the RFID tag information from adversaries. Accordingly, a casual attacker with time-limited access to the RFID tag, and thus unable to obtain more than a few emissions, will be unable to reconstruct the RFID tag information. For a similar technique, see M. Langheinrich and R. Marti, “Practical minimalist cryptography for RFID privacy,” In submission, 2007.